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Elastic Scattering and Transport Coefficients for a Quark Plasma in $SU_f(3)$ at Finite Temperatures

The temperature dependence of the elastic scattering processes $qq'\to qq'$ and $q\bar q'\to q\bar q'$, with $q, q' = u, d, s$ is studied as a function of the scattering angle and the center of mass energy of the collision within the framework of the $SU_f(3)$ Nambu--Jona--Lasinio model. Critical scattering at threshold is observed in the $q\bar q'\to q\bar q'$ process, leading to an enhancement of the cross section as occurs in the phenomenon of critical opalescence. Transport properties such as viscosity, mean free paths and thermal relaxation times are calculated. Strangeness enhancement is investigated via the chemical relaxation times, which are found to be considerably higher than those calculated via perturbative QCD. A comparison with the experimental values for the strangeness enhancement in $S+S$ collisions leads to an upper limit of 4~fm/$c$ for the lifetime of the plasma.